Question

Simplify https://media.glynlyon.com/g_alg02_ccss_2013/7/img_alg02u07t19d_23.gif to get a complex number in standard a + bi form.

Answer 1

@vishweshshrimali5

Answer 2

Multiply by (6-5i) on both numerator and denominator

Answer 3

-30 - 25i

Answer 4

No no

Answer 5

Try again

Answer 6

36-25i

Answer 7

See:

\[\large{\cfrac{1}{6+5i} = \cfrac{6-5i}{(6+5i)(6-5i)} = \cfrac{6-5i}{6^2 - (5i)^2}}\]
\[\large{= \cfrac{6-5i}{36 - 25i^2}}\]

Now, \(\large{i^2 = -1}\)
Thus,

\[\large{\cfrac{1}{6+5i} = \cfrac{6-5i}{36+25} = \cfrac{6-5i}{61}}\]

Answer 8

Ok I get it now, thank you